Signals may be used to transmit data over distances. In optical communication systems, for example, data may be modulated on one or more optical wavelengths to produce modulated optical signals that may be transmitted over optical waveguides such as optical fibers. One modulation scheme that may be used in optical communication systems is phase shift keying in which data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength represents symbols encoding one or more bits. In a binary phase-shift keying (BPSK) modulation scheme, for example, two phases may be used to represent 1 bit per symbol. In a quadrature phase-shift keying (QPSK) modulation scheme, four phases may be used to encode 2 bits per symbol. Other phase shift keying formats include differential phase shift keying (DPSK) formats and variations of phase shift keying and differential phase shift keying formats, such as return-to-zero DPSK (RZ-DPSK). Another modulation format is quadrature amplitude modulation (QAM) in which information is modulated onto both phase and amplitude of a transmitted signal.
To receive the data, the signals may be detected and demodulated. In phase modulated optical communication systems, for example, coherent optical receivers may use coherent detection to detect modulated optical signals and may provide sensitivity advantages over receivers using non-coherent detection. Digital signal processing (DSP) may be implemented in such systems for processing the received signals to provide a demodulated data. Digital signal processing of the received signal provides speed and flexibility and may be used to perform a variety of functions including estimation of the carrier phase of the received signals and data detection using the estimated carrier phase.
Distortion of a signal (e.g., during transmission), however, may adversely affect the integrity of the data that is obtained after detecting and demodulating the signal. In optical communications systems using phase modulation schemes, nonlinear effects, such has self phase modulation (SPM), may cause phase distortion in the modulated signal, which may significantly degrade coherent-detection performance and diminish the receiver-sensitivity advantage that coherent detection has over non-coherent detection. The degradation in BPSK signals is described in greater detail in Yi Cai, et. al., “On Performance of Coherent Phase-Shift-Keying Modulation in 40 Gb/s Long-Haul Optical Fiber Transmission Systems”, Optical Fiber Communication and the National Fiber Optic Engineers Conference, 2006, paper JThB 11 (March 2006), which is fully incorporated herein by reference.
The distortion in a modulated signal, such as phase distortion in a modulated optical signal, may often be dependent on the data pattern or bit-pattern. FIGS. 9 and 10 illustrate bit-pattern dependent phase distortions that may occur in an optical communication system based on a single-channel nonlinear propagation simulation. FIG. 9 shows a constellation diagram of a distorted BPSK signal in which the constellation points extend above and below the real axis, indicating the effect of phase distortion. FIG. 10 shows phase distortions corresponding to various bit patterns and illustrates how the phase distortions are dependent on bit pattern.
Methods have been proposed for mitigating the performance penalty induced by data-pattern dependent distortion such as nonlinear phase distortion in optical coherent receivers. One method compensates the nonlinear phase distortion based on estimated phase distortion as a function of received signal intensity, for example, as described in K. Ho and J. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” Journal of Lightwave Technology, 22, 779-783 (2004) and in K. Kikuchi “Electronic Post-compensation for nonlinear Phase Fluctuations in a 1000-km 20-Gb/s Optical Quadrature Phase-shift Keying Transmission System Using the Digital Coherent Receiver,” Optics Express, Vol. 16, No. 2, 2007, which are fully incorporated herein by reference. This method may fail, however, when optical signal intensity changes significantly during propagation, which is often the case in optical communication systems employing a practical chromatic dispersion map.
Another method compensates nonlinear distortion by digital backpropagation, for example, as described in X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Optics Express, vol. 16, no. 2, pp. 880-888, Jan. 21, 2008, and in E. Ip, A. P. T. Lau, D. J. Barros and J. M. Kahn, “Compensation of chromatic dispersion and nonlinearity using simplified digital backpropagation,” Proc. of OSA Topical Meeting on Coherent Optical Technologies and Applications, Boston, Mass., Jul. 13-16, 2008, which are fully incorporated herein by reference. This backpropagation method involves complicated calculations and may not be practical in 10-100 Gb/s optical transmissions.